I'd like to list all videos that are only visible to me on Vimeo: how can I achieve that?
When building an off site list of Vimeo videos, you will need to use the API.
Vimeo's new API has a lot of the features you need, and you can get started here: https://developer.vimeo.com/api/start
The above link will walk you through app creation, and then the endpoint varies based on the videos you want to see. It's pretty intuitive though, so start here: https://developer.vimeo.com/api/endpoints
If you want to see your videos, request
/me/videos. If you want to see all videos in the staff picks channel, request
Make sure to read the Authentication documentation, I expect you are building a Single User application and can hard code your authentication token into your app.